Enable Ambient Occlusion (AO) in Cycles?
I finally found the solution: You don't need to enable Ambient Occlusion in the "World"-settings (since this just brightens your image): just enable it in the "View Layer"-settings as a pass. Then, in the Compositor, add a Color Balance node (or some other color node that allows you to change the darkness of the AO pass) and connect it to the AO output of the Render Layers node. Then, connect the output of the Color Balance node and the Image output of the Render Layers node to a Multiply (Mix) node, and then finally connect the output of the Multiply (Mix) node to a File Output node. This way you can manually control the AO in Cycles.